Why does Florida does not pay state tax?

All levels of government have their own type of funding to pay their expenses. The federal government uses mostly income and excise taxes. City and county governments mostly use property taxes. Some cities use a sales taxes in addition to property taxes.

States vary. Some states, like Oregon, use primarily income taxes and don't have a sales tax. Other states, like Florida, use mainly sales taxes and don't have an income tax. Most states, use a combination and have both income and sales taxes. Some states only tax businesses and not individuals, like Alaska who gets tax income from corporations and businesses only and doesn't have a sales tax. Many states also have other types of taxes in addition to their main source of taxes (use, luxury, lodging, etc).

This is how these various levels of government get their income to operate and run programs, provide services, and pay employees.